Network. We consider \(n=20\)  computing nodes connected as an Erdős-Rényi graph [1]}, where any two nodes are linked with probability \(2\text{ln}(n)/n\) . Note that \(\text{ln}(n)/n\)  is the lowest probability to ensure a connected graph. Then, we use the Metropolis rule [2]} to construct \(W\)  to satisfy assum2. All results are repeated 10 times on different graphs, and we report their average performance.
